Question: Rewrite as a simplified fraction. ${0.3\overline{34} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 334.3434...\\ 10x &= 3.3434...\end{align*}}$ Subtracting the two equations, we have: ${990x = 331}$ ${x = \dfrac{331}{990}} $